CSCE 355 Foundations of Computation Lecture 4 NFAs

CSCE 355 Foundations of Computation Lecture 4 NFAs Topics: n Induction review n DFAs again NFAs Delta, delta hat Strings accepted, languages accepted n n n Sept 8, 2008

Induction Revisited – 2– CSCE 355 Fall 2008

Induction HW – 3– CSCE 355 Fall 2008

Common Mistakes in HW – 4– CSCE 355 Fall 2008

Induction Pseudo Pop Quiz – 5– CSCE 355 Fall 2008

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Review DFA • Delta hat • Path determined by input • DFA accepting a string • Language accepted by DFA – 8– CSCE 355 Fall 2008

Pigeon Hole Principle application – 9– CSCE 355 Fall 2008

Homework from Email – 10 – CSCE 355 Fall 2008

DFA Simulation in Ruby • # !/usr/bin/ruby • #MMM 9/5/2008 • # Simulation/Implementation of a DFA in Ruby • # the DFA M=(Q, Sigma, delta, q 0, F) • numstates = 4 # Q = [0, 1, 2, 3] • alphabet = ['a', 'b'] # Sigma = {a, b} • # delta implemented as function • q 0 = 0 # Start state is state 0 • accepting. State = Array. new(4, 0) • accepting. State[1] = 1 – 11 – #F={1} CSCE 355 Fall 2008

def delta(state, input. Char) case when state == 0 case when input. Char == 'a' then return 1; when input. Char == 'b' then return 3 end when state == 1 case when input. Char == 'a' then return 2 when input. Char == 'b' then return 0 end. . . else return 999 end – 12 – CSCE 355 Fall 2008

# Start Simulation state = 0 print "alphabet = #{alphabet}n" print "accepting. State = #{accepting. State}n" # print "Enter the input string: " line = gets puts "line=#{line}" inp = line. chomp. split(//) – 13 – CSCE 355 Fall 2008

# foreach x in inp. each { |x| break x if x =="n" ###break x if x =='X' nextstate = delta(state, x) print "delta(=#{state}, char=#{x}) = #{nextstate}n" state = nextstate } if accepting. State[state] == 1 then puts "Accept" else puts "Reject" end – 14 – CSCE 355 Fall 2008

Example 2. 4 – 15 – CSCE 355 Fall 2008

Exercise 2. 2. 4 – 16 – CSCE 355 Fall 2008

DFA that accepts Union – 17 – CSCE 355 Fall 2008

Nondeterministic Finite Automata – 18 – CSCE 355 Fall 2008

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